Approximation of a Solidification Problem

• Autorzy: Aboulaich R. , Haggouch I. , Souissi A.
• Języki publikacji: EN

Abstrakty

EN

A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocci, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al.., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2-rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.

Słowa kluczowe

EN

Stefan problem; free boundary; shape optimization; Euler method; finite element method

PL

optymalizacja; metoda elementów skończonych

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: Vol. 11, no 4
• Strony: 921--955
• Opis fizyczny: Bibliogr. 19 poz., tab., wykr.

Twórcy

autor

Aboulaich R.

autor

Haggouch I.

autor

Souissi A.

• Universite Mohamed V Ecole Mohammadia d'Ingenieurs L.E.R.M.A Av. Ibn Sina, B.P. 765 AGDAL, Rabat, Morocco,